Subdivision surface not working properly
in the Subdivision Surface modifier, the Render value is for the definitive render, the one you get when you press the Render button in the Properties panel > Render > Render, it is not for the Rendered display option you have on the dropdown menu of the horizontal menu bar of the 3D View, this one takes the View value into account. It's a bit confusing, yes.

Also, in Properties panel > Render > Sampling > Samples, you choose the final Render sampling value and the 3D view Preview sampling value. You generally don't work your 3D view with a value as high as the Render value because it would take too much time. But in Blender 2.8 you'll have Eevee which is quite fast.